Abstract

The use of the generalized Lorenz–Mie theory that describes the interaction between a spherical particle and an arbitrarily shaped beam requires knowledge of the beam-shape coefficients (BSC’s) that describe the illuminating beam. Classically, these BSC’s are evaluated from an a priori mathematical description of the illuminating beam. We propose a method that relies on intensity measurements along the beam axis that permits one to measure directly the BSC’s of an actual beam in the laboratory.

© 1998 Optical Society of America

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References

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  1. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  2. F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
    [CrossRef] [PubMed]
  3. G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Charact. 11, 133–145 (1994).
    [CrossRef]
  4. F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
    [CrossRef]
  5. G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
    [CrossRef]
  6. K. F. Ren, G. Gréhan, G. Gouesbet, “On prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
    [CrossRef] [PubMed]
  7. H. Polaert, G. Gréhan, G. Gouesbet, “Reverse radiation pressure and standard beams,” Appl. Opt. 37, 2435–2440 (1998).
    [CrossRef]
  8. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  9. J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
    [CrossRef] [PubMed]
  10. J. A. Lock, J. T. Hodges, “Far field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle,” Appl. Opt. 35, 4283–4290 (1996).
    [CrossRef] [PubMed]
  11. J. A. Lock, J. T. Hodges, “Far field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle,” Appl. Opt. 35, 6605–6616 (1996).
    [CrossRef] [PubMed]
  12. G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz-Mie theory and the density-matrix approach: I. Measurements,” Part. Part. Syst. Charact. 14, 12–20 (1997).
  13. G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz-Mie theory and the density-matrix approach: II. The density-matrix approach,” Part. Part. Syst. Charact. 14, 88–92 (1997).
  14. G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
    [CrossRef] [PubMed]
  15. G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
    [CrossRef]
  16. G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
    [CrossRef]
  17. G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gn in the generalized Lorenz-Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
    [CrossRef] [PubMed]
  18. G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
    [CrossRef]
  19. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing, (Cambridge U. Press, Cambridge, UK, 1986).
  20. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965).
    [CrossRef]
  21. B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
    [CrossRef]
  22. Y. Suzaki, A. Tachibana, “Measurement of the μm sized radius of Gaussian laser beam using the scanning knife-edge,” Appl. Opt. 14, 2809–2810 (1975).
    [CrossRef] [PubMed]
  23. D. K. Cohen, B. Little, F. S. Luecke, “Techniques for measuring 1-μm diam Gaussian beams,” Appl. Opt. 23, 637–640 (1984).
    [CrossRef] [PubMed]
  24. M. T. Gale, H. Meier, “Rapid evaluation of submicron laser spots,” RCA Rev. 46, 56–69, (1985).
  25. B. Cannon, T. S. Gardner, D. K. Cohen, “Measurements of 1-μm diam beams,” Appl. Opt. 25, 2981–2983 (1986).
    [CrossRef] [PubMed]
  26. J. C. Knight, N. Dubreuil, V. Sandoghar, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Characterizing whispering-gallery modes in microspheres by direct observation of the optical standing-wave pattern in the near field,” Opt. Lett. 21, 698–700 (1996).
    [CrossRef] [PubMed]

1998 (1)

1997 (2)

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz-Mie theory and the density-matrix approach: I. Measurements,” Part. Part. Syst. Charact. 14, 12–20 (1997).

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz-Mie theory and the density-matrix approach: II. The density-matrix approach,” Part. Part. Syst. Charact. 14, 88–92 (1997).

1996 (6)

1995 (3)

1994 (1)

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Charact. 11, 133–145 (1994).
[CrossRef]

1990 (1)

1989 (1)

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

1988 (2)

1986 (2)

1985 (1)

M. T. Gale, H. Meier, “Rapid evaluation of submicron laser spots,” RCA Rev. 46, 56–69, (1985).

1984 (1)

1982 (1)

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

1979 (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

1975 (1)

1965 (1)

Angelova, M. I.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Brenn, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Cannon, B.

Cohen, D. K.

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Domnick, J.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Dubreuil, N.

Durst, F.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Charact. 11, 133–145 (1994).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing, (Cambridge U. Press, Cambridge, UK, 1986).

Gale, M. T.

M. T. Gale, H. Meier, “Rapid evaluation of submicron laser spots,” RCA Rev. 46, 56–69, (1985).

Gardner, T. S.

Girasole, T.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Gouesbet, G.

H. Polaert, G. Gréhan, G. Gouesbet, “Reverse radiation pressure and standard beams,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz-Mie theory and the density-matrix approach: I. Measurements,” Part. Part. Syst. Charact. 14, 12–20 (1997).

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz-Mie theory and the density-matrix approach: II. The density-matrix approach,” Part. Part. Syst. Charact. 14, 88–92 (1997).

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “On prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
[CrossRef] [PubMed]

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Charact. 11, 133–145 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gn in the generalized Lorenz-Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

Gréhan, G.

H. Polaert, G. Gréhan, G. Gouesbet, “Reverse radiation pressure and standard beams,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “On prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
[CrossRef] [PubMed]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Charact. 11, 133–145 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gn in the generalized Lorenz-Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

Hare, J.

Haroche, S.

Hodges, J. T.

Knight, J. C.

Kogelnik, H.

Lefevre-Seguin, V.

Little, B.

Lock, J. A.

Luecke, F. S.

Maheu, B.

Martinot-Lagarde, G.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Meier, H.

M. T. Gale, H. Meier, “Rapid evaluation of submicron laser spots,” RCA Rev. 46, 56–69, (1985).

Naqwi, A.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Charact. 11, 133–145 (1994).
[CrossRef]

Onofri, F.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

Polaert, H.

Pouligny, B.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing, (Cambridge U. Press, Cambridge, UK, 1986).

Presser, C.

Raimond, J. M.

Ren, K. F.

Sandoghar, V.

Suzaki, Y.

Tachibana, A.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing, (Cambridge U. Press, Cambridge, UK, 1986).

Tropea, C.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing, (Cambridge U. Press, Cambridge, UK, 1986).

Xu, T. H.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Appl. Opt. (13)

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
[CrossRef] [PubMed]

J. A. Lock, J. T. Hodges, “Far field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle,” Appl. Opt. 35, 4283–4290 (1996).
[CrossRef] [PubMed]

J. A. Lock, J. T. Hodges, “Far field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle,” Appl. Opt. 35, 6605–6616 (1996).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, G. Gouesbet, “On prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

H. Polaert, G. Gréhan, G. Gouesbet, “Reverse radiation pressure and standard beams,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gn in the generalized Lorenz-Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965).
[CrossRef]

Y. Suzaki, A. Tachibana, “Measurement of the μm sized radius of Gaussian laser beam using the scanning knife-edge,” Appl. Opt. 14, 2809–2810 (1975).
[CrossRef] [PubMed]

D. K. Cohen, B. Little, F. S. Luecke, “Techniques for measuring 1-μm diam Gaussian beams,” Appl. Opt. 23, 637–640 (1984).
[CrossRef] [PubMed]

B. Cannon, T. S. Gardner, D. K. Cohen, “Measurements of 1-μm diam beams,” Appl. Opt. 25, 2981–2983 (1986).
[CrossRef] [PubMed]

J. Opt. (Paris) (1)

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

Opt. Lett. (1)

Part. Part. Syst. Charact. (4)

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz-Mie theory and the density-matrix approach: I. Measurements,” Part. Part. Syst. Charact. 14, 12–20 (1997).

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz-Mie theory and the density-matrix approach: II. The density-matrix approach,” Part. Part. Syst. Charact. 14, 88–92 (1997).

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Charact. 11, 133–145 (1994).
[CrossRef]

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, C. Tropea, “Phase Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Phys. Rev. A (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Pure Appl. Opt. (1)

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

RCA Rev. (1)

M. T. Gale, H. Meier, “Rapid evaluation of submicron laser spots,” RCA Rev. 46, 56–69, (1985).

Other (1)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing, (Cambridge U. Press, Cambridge, UK, 1986).

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Figures (10)

Fig. 1
Fig. 1

Geometry of the problem to be solved.

Fig. 2
Fig. 2

Measured Gaussian profile and its reconstruction.

Fig. 3
Fig. 3

Comparison of theoretical and experimental (measured) special BSC’s.

Fig. 4
Fig. 4

Original and reconstructed data for a general on-axis case (z 0 = 2λ).

Fig. 5
Fig. 5

Original and reconstructed data for a general on-axis case (z 0 = 10λ).

Fig. 6
Fig. 6

Original and reconstructed data for a general on-axis case (z 0 = 15λ).

Fig. 7
Fig. 7

Comparison of theoretical and reconstructed transverse profiles.

Fig. 8
Fig. 8

Comparison of theoretical and reconstructed longitudinal profiles (z 0 = 15λ). The reconstruction domain is larger than the measurement domain.

Fig. 9
Fig. 9

Comparison of theoretical and reconstructed longitudinal profiles. O P is located outside the measurement domain (z 0 = 100λ).

Fig. 10
Fig. 10

Dependence of the inversion procedure on the number of unknown BSC’s.

Equations (33)

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S z = k ω μ 0   E 0 E 0 * K 2 + 1 4 r 2 × Re cos   θ   n = 1 m = 1   c n pw c m pw * g n g m * A n B m * + sin   θ   n = 1 m = 1   c n pw c m pw * g n g m * m m + 1 B n Ψ m 1 P m 1 ,
A n = d r Ψ n 1 kr d r   τ n cos   θ - ikr Ψ n 1 kr π n cos   θ ,
B n = d r Ψ n 1 kr d r   π n cos   θ - ikr Ψ n 1 kr τ n cos   θ ,
P n 1 cos   θ = - sin   θ   d P n cos   θ d   cos   θ ,
τ n cos   θ = d d θ   P n 1 cos   θ ,
π n cos   θ = P n 1 cos   θ sin   θ .
c n pw = 1 ik - i n 2 n + 1 n n + 1 .
S z = r 2 Re n = 1 m = 1   c n pw c m pw * g n g m * A n B m * ,
k ω μ 0 E 0 E 0 * 2 = 1 .
π n 1 = τ n 1 = Γ n ,
π n - 1 = - 1 n - 1 Γ n ,
τ n - 1 = - 1 n Γ n ,
Γ n = - n n + 1 2 .
A n B m * = Γ n Γ m n + m + 1 D nm 1 + i n + m D nm 2 ,
D nm 1 = d r Ψ n 1 kr d r d r Ψ m 1 kr d r + k 2 r 2 Ψ n 1 kr Ψ m 1 kr ,
D nm 2 = kr d r Ψ n 1 kr d r   Ψ m 1 kr - d r Ψ m 1 kr d r   Ψ n 1 kr .
S z =   Re n = 1 m = 1   a nm g n g m * ,
a nm = 1 k 2 r 2   i m - n n + 1 / 2 m + 1 / 2 × n + m + 1 D nm 1 + i n + m D nm 2 .
S i = S i g 1 ,   g 2 , ,   g n ,     i = 1 , ,   q ,
f i = S i g 1 ,   g 2 , g n - S i = 0 ,     i = 1 q ,
f g + δ g = f g + δ gf g + f g 2 δ g 2 + .
f g + δ g = 0 .
δ g = - f g f g .
j   α ij δ g j = β i ,
α ij = d f i d g j ,     β i = - f i .
α ij = d f i d g j = r = 1 n   2 g r Re a jr i ,
β i = - f i = S i - r = 1 n p = 1 n   g r g p Re a rp i ,
g n = R n + iI n ,
j α ij δ R j + γ ij δ I j = β i ,
α ij = d f i d R j ,     γ ij = d f i d I j .
α ij = 2   r = 1 n   R r Re a jr i + I r Im a jr i ,
γ ij = 2   r = 1 n   I r Re a jr i - R r Im a jr i ,
β i = - f i = S i - r = 1 n p = 1 n Re a rp i R r R p + I r I p - Im a rp i I r R p - R r I p .

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